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telo118 [61]
3 years ago
7

Solve.

Mathematics
1 answer:
KengaRu [80]3 years ago
7 0

Answer:

$11,113.20

$41,377.20

Step-by-step explanation:

The equation that would be used to represent the increase in rent every month is :

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

Rent paid in the first year = 9600

Rent paid in the second year = 9600 x (1.05) = 10,080

Rent paid in the third year = 9600 x (1.05)^2 = 10,584

Rent paid in the fourth year = 9600 x (1.05)^3 = 11,113.20

Rent paid in4 years is the sum of the rents paid each year :

9600 + 10,080 + 10,584 + 11,113.20 = $41,377.2

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A force of 12 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching i
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Answer:

Work done in stretching the spring = 7.56 lb-ft.

Step-by-step explanation:

Normal length of the spring = 8 in or \frac{8}{12} ft

= \frac{2}{3} ft

If the spring has been stretched to 11 inch then the stretched length of the spring is = 11 in

= \frac{11}{12} ft

Force applied to stretch the spring = 12 lb

By Hook's law,

F = kx [where k is the spring constant and x = length by which the spring is stretched]

12 = k(\frac{2}{3})

k = 18

Work done (W) to stretch the spring by \frac{11}{12} ft will be

W = \int\limits^\frac{11}{12} _0 {kx} \, dx

    = \int\limits^\frac{11}{12} _0 {(18x)} \, dx

    = 18[\frac{x^{2}}{2}]^{\frac{11}{12}}_0

    = 9(\frac{11}{12})²

    = 7.56 lb-ft

6 0
3 years ago
Mercedes bought 2 1/2 pounds of blueberries and her son ate 1/4 the blueberries how many pounds of blueberries Are left?
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ANDREA IS A VERY GOOD STUDENT. THE PROBABILITY THAT SHE STUDIES AND PASSES HER MATHEMATICS TEST IS 17/20. IF THE PROBABILITY THA
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Let B be the event that Andrea passes her test, and let A be the event 
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Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average u
soldier1979 [14.2K]

x = f ( p ) = \frac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } } \\\\ \qquad { p ( t ) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \quad ( 0 \leq t \leq 60 ) }

Answer:

12.0 tablet computers/month

Step-by-step explanation:

The average price of the tablet 25 months from now will be:

p ( 25) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { 25 } } + 200 \\= \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \times 5 } + 200\\\\=\dfrac { 400 } { 1 + \dfrac { 5 } { 8 } } + 200\\p(25)=\dfrac { 5800 } {13}

Next, we determine the rate at which the quantity demanded changes with respect to time.

Using Chain Rule (and a calculator)

\dfrac{dx}{dt}= \dfrac{dx}{dp}\dfrac{dp}{dt}

\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}

\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}

Therefore:

\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]

Recall that at t=25, p(25)=\dfrac { 5800 } {13} \approx 446.15

Therefore:

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The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.

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